Question: Exercise 6. Let (X, d) be a metric space. Given E C X, let E be the set of interior points of E. (The

Exercise 6. Let (X, d) be a metric space. Given E C

Exercise 6. Let (X, d) be a metric space. Given E C X, let E be the set of interior points of E. (The set E is called the interior of E.) (a) If GCE is open, prove that G C E. (b) Prove that E is an open set. (c) From the previous two parts, deduce that E is the union of all open subsets of E.

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